Affiliations: [a] Faculty of Mechanical Engineering, University of Niš, A. Medvedeva 14, 18000 Niš, Serbia. [email protected] | [b] Int. Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), University of Abomey-Calavi, 072 B.P. 50 Cotonou, Republic of Benin, Africa. [email protected] (with copy to [email protected]) | [c] Dunarea de Jos University of Galati, Romania. [email protected]
Correspondence:
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Address for correspondence: Faculty of Mechanical Engineering, A. Medvedeva 14, 18000 Niš, Serbia.
Abstract: This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also draw attention to its possible applications in other (constructive) mathematics disciplines, in computer science, social sciences, economics, etc. Another important goal of this paper is to provide a clear, understandable picture of constructive semigroups with apartness in Bishop’s style both to (classical) algebraists and the ones who apply algebraic knowledge.
Keywords: Semigroup with apartness, set with apartness, co-quasiorder, co-equivalence, co-congruence
